Confusion over trig equations and sine/cosine

I'm trying to make sense of a video assigned by my professor on sine and cosine equations . The problem is as follows

sin 2x + cos x = 0

In the video he says sin 2x can be changed to 2 sin x + cos x = 0. And then he says 2 sin x can be substituted with

2 sin x cos x + cos x = 0, which can then be factored by grouping.

That's where I'm confused. Why does 2 sin x magically equal 2 sin x cos x all of a sudden? What am I missing here? I can solve the equation the rest of the way following his steps, but I don't understand why that substitution can be made. Any helpful replies would be most welcome.

Re: Confusion over trig equations and sine/cosine

I'm trying to make sense of a video assigned by my professor on sine and cosine equations . The problem is as follows

sin 2x + cos x = 0

In the video he says sin 2x can be changed to 2 sin x + cos x = 0. And then he says 2 sin x can be substituted with

2 sin x cos x + cos x = 0, which can then be factored by grouping.

That's where I'm confused. Why does 2 sin x magically equal 2 sin x cos x all of a sudden? What am I missing here? I can solve the equation the rest of the way following his steps, but I don't understand why that substitution can be made. Any helpful replies would be most welcome.

either the video or your interpretation of it is incorrect. It should go like this

Re: Confusion over trig equations and sine/cosine

I'm trying to make sense of a video assigned by my professor on sine and cosine equations . The problem is as follows

sin 2x + cos x = 0

In the video he says sin 2x can be changed to 2 sin x + cos x = 0. And then he says 2 sin x can be substituted with

2 sin x cos x + cos x = 0, which can then be factored by grouping.

That's where I'm confused. Why does 2 sin x magically equal 2 sin x cos x all of a sudden? What am I missing here? I can solve the equation the rest of the way following his steps, but I don't understand why that substitution can be made. Any helpful replies would be most welcome.